Agro-Ecological Control of a Pest-Host System: Preventing Spreading

We consider an agro-ecologically motivated coupling between a prey-predator system and vector-borne epidemic system. The coupled contains one ODE, two reaction-diffusion PDEs, reaction-diffusion–advection PDE; it has no complete variational or monotonic structure coefficients are spatially heterogeneous. study the long-time behavior of solutions Cauchy–Neumann problem, which turns out to be largely decided by linear stability criterion but still involves nonlinear subtleties. Then we optimal control problem. Although remains elusive analytically, show numerically variety outcomes strong impact initial conditions.